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Preprint-No.: <   363   >   Published in: April 2013   PDF-File: IGPM363_k.pdf
Title:Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations
Authors:Markus Bachmayr, Wolfgang Dahmen
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive ap- proximation in a basis. Under fairly general assumptions, we obtain a rigorous con- vergence analysis, where all parameters required for the execution of the methods depend only on the underlying infinite-dimensional problem, but not on a concrete discretization. Under certain assumptions on the rates for the involved low-rank ap- proximations and basis expansions, we can also give bounds on the computational complexity of the iteration as a function of the prescribed target error. Our theo- retical findings are illustrated and supported by computational experiments. These demonstrate that problems in very high dimensions can be treated with controlled solution accuracy.
Keywords:Low–rank tensor approximation, adaptive methods, high–dimensional operator equations, computational complexity
DOI: 10.1007/S10208-013-9187-3
Publication:Foundations of Computational Mathematics
15(2015), 839-898

Oberwolfach reports : OWR 10(3), 2179-2257 (2013)
DOI: 10.4171/OWR/2013/39